{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!--BOOK_INFORMATION-->\n",
    "<a href=\"https://www.packtpub.com/big-data-and-business-intelligence/machine-learning-opencv\" target=\"_blank\"><img align=\"left\" src=\"data/cover.jpg\" style=\"width: 76px; height: 100px; background: white; padding: 1px; border: 1px solid black; margin-right:10px;\"></a>\n",
    "*This notebook contains an excerpt from the book [Machine Learning for OpenCV](https://www.packtpub.com/big-data-and-business-intelligence/machine-learning-opencv) by Michael Beyeler.\n",
    "The code is released under the [MIT license](https://opensource.org/licenses/MIT),\n",
    "and is available on [GitHub](https://github.com/mbeyeler/opencv-machine-learning).*\n",
    "\n",
    "*Note that this excerpt contains only the raw code - the book is rich with additional explanations and illustrations.\n",
    "If you find this content useful, please consider supporting the work by\n",
    "[buying the book](https://www.packtpub.com/big-data-and-business-intelligence/machine-learning-opencv)!*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!--NAVIGATION-->\n",
    "< [Understanding the k-NN Classifier](03.02-Understanding-the-k-NN-Algorithm.ipynb) | [Contents](../README.md) | [Applying Lasso and Ridge Regression](03.04-Applying-Lasso-and-Ridge-Regression.ipynb) >"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Using Regression Models to Predict Continuous Outcomes\n",
    "\n",
    "Now let's turn our attention to a **regression** problem. Regression is all about predicting continuous outcomes rather than predicting\n",
    "discrete class labels."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using linear regression to predict Boston housing prices\n",
    "\n",
    "The easiest regression model is called **linear regression**. The idea behind linear regression is\n",
    "to describe a target variable (such as Boston house pricing) with a linear combination of\n",
    "features.\n",
    "\n",
    "If you want to understand how the math behind linear regression works, please refer to the book (p.65ff.).\n",
    "\n",
    "To get a better understanding of linear regression, we want to build a simple model that can\n",
    "be applied to one of the most famous machine learning datasets known as the **Boston\n",
    "housing prices dataset**. Here, the goal is to predict the value of homes in several Boston\n",
    "neighborhoods in the 1970s, using information such as crime rate, property tax rate,\n",
    "distance to employment centers, and highway accessibility."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Loading the dataset\n",
    "\n",
    "We can again thank scikit-learn for easy access to the dataset. We first import all the\n",
    "necessary modules, as we did earlier:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import cv2\n",
    "\n",
    "from sklearn import datasets\n",
    "from sklearn import metrics\n",
    "from sklearn import model_selection\n",
    "from sklearn import linear_model\n",
    "\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('ggplot')\n",
    "plt.rcParams.update({'font.size': 16})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then, loading the dataset is a one-liner:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "boston = datasets.load_boston()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The structure of the boston object is identical to the `iris` object. We can get more information about the dataset by looking at the fields of the `boston` object:\n",
    "- `DESCR`: Get a description of the data\n",
    "- `data`: The actual data, <`num_samples` x `num_features`>\n",
    "- `feature_names`: The names of the features\n",
    "- `target`: The class labels, <`num_samples` x 1>\n",
    "- `target_names`: The names of the class labels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['DESCR', 'data', 'feature_names', 'target']"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dir(boston)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The dataset contains a total of 506 data points, each of which has 13 features:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(506, 13)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boston.data.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Of course, we have only a single target value, which is the housing price:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(506,)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boston.target.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Training the model\n",
    "\n",
    "Believe it or not, OpenCV does not offer any good implementation of linear regression.\n",
    "Some people online say that you can use `cv2.fitLine`, but that is different. This is a\n",
    "perfect opportunity to get familiar with scikit-learn's API:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "linreg = linear_model.LinearRegression()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the preceding command, we want to split the data into training and test sets. We are free\n",
    "to make the split as we see fit, but usually it is a good idea to reserve between 10 percent\n",
    "and 30 percent for testing. Here, we choose 10 percent, using the `test_size` argument:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = model_selection.train_test_split(\n",
    "    boston.data, boston.target, test_size=0.1, random_state=42\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In scikit-learn, the `train` function is called `fit`, but otherwise behaves exactly the same as\n",
    "in OpenCV:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "linreg.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can look at the mean squared error of our predictions by comparing the true housing\n",
    "prices, `y_train`, to our predictions, `linreg.predict(X_train)`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "22.739484154236614"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "metrics.mean_squared_error(y_train, linreg.predict(X_train))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `score` method of the `linreg` object returns the coefficient of determination (R\n",
    "squared):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.73749340919011974"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "linreg.score(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Testing the model\n",
    "\n",
    "In order to test the **generalization performance** of the model, we calculate the mean\n",
    "squared error on the test data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y_pred = linreg.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "15.010997321630107"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "metrics.mean_squared_error(y_test, y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We note that the mean squared error is a little lower on the test set than the training set.\n",
    "This is good news, as we care mostly about the test error. However, from these numbers, it\n",
    "is really hard to understand how good the model really is. Perhaps it's better to plot the\n",
    "data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f08d2a34eb8>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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SClnkMpTHH38cpaWl+Pbbb3HZZZdhwoQJOOmkk/D73/8ePM8DiLoY169fj3vvvRfTpk3D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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f08d4a72ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(y_test, linewidth=3, label='ground truth')\n",
    "plt.plot(y_pred, linewidth=3, label='predicted')\n",
    "plt.legend(loc='best')\n",
    "plt.xlabel('test data points')\n",
    "plt.ylabel('target value')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This makes more sense! Here we see the ground truth housing prices for all test samples\n",
    "in blue and our predicted housing prices in red. Pretty close, if you ask me. It is interesting\n",
    "to note though that the model tends to be off the most for really high or really low housing\n",
    "prices, such as the peak values of data point 12, 18, and 42. We can formalize the amount of\n",
    "variance in the data that we were able to explain by calculating $R^2$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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nhg8fjp+fH76+vpYuS6TIldnlavJiZWXF1KlTad68Oe+99x7z58/HysqKmTNn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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f08d2975860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(y_test, y_pred, 'o')\n",
    "plt.plot([-10, 60], [-10, 60], 'k--')\n",
    "plt.axis([-10, 60, -10, 60])\n",
    "plt.xlabel('ground truth')\n",
    "plt.ylabel('predicted')\n",
    "\n",
    "scorestr = r'R$^2$ = %.3f' % linreg.score(X_test, y_test)\n",
    "errstr = 'MSE = %.3f' % metrics.mean_squared_error(y_test, y_pred)\n",
    "plt.text(-5, 50, scorestr, fontsize=12)\n",
    "plt.text(-5, 45, errstr, fontsize=12);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If our model was perfect, then all data points would lie on the dashed diagonal, since\n",
    "`y_pred` would always be equal to `y_true`. Deviations from the diagonal indicate that the\n",
    "model made some errors, or that there is some variance in the data that the model was not\n",
    "able to explain. Indeed, $R^2$ indicates that we were able to explain 76 percent of the scatter in\n",
    "the data, with a mean squared error of 15.011. These are some hard numbers we can use to\n",
    "compare the linear regression model to some more complicated ones."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!--NAVIGATION-->\n",
    "< [Understanding the k-NN Classifier](03.02-Understanding-the-k-NN-Algorithm.ipynb) | [Contents](../README.md) | [Applying Lasso and Ridge Regression](03.04-Applying-Lasso-and-Ridge-Regression.ipynb) >"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.3"
  }
 },
 "nbformat": 4,
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